How can I link one face data to multiple faces for uv mapping?
Quick answer: No, as far as I know there is no way to copy UV data between chunks of mesh belonging to the same object.

If the spokes are all the same they should be kept as separate objects, as instances sharing the same object data.

Anyway if you still want them as one object then


Select your spokes object
Enter edit mode
Select one spoke
Separate it from the main object using P
Exit edit mode and enter edit mode on your separate spoke object
Edit it as desired, and assign it the correct UV coordinates.
Now place the 3D cursor at the center of the wheel/spokes
Press . (Period key) to rotate around the 3D cursor
Copy your spoke object with Alt + D to make instances
Press R to rotate around the 3D cursor
Adjust the angle as desired and place as many copies as necessary


You may now join them again as before, and they will all have the same UV coordinates, although I think there are better workflows.

Either keep them as separate object instances sharing the same object data and that will keep them in sync automatically, or alternatively, if you need them as a single object, use an Array Modifier.


Delete all but one instance, and add an Array Modifier to the
remaining one. Set it to object offset.
Now with the 3D cursor still in the center of the tire add a new
empty object
Rotate it the same amount of degrees you would rotate one of the spokes.
Assign this empty as object offset to the array modifier
Adjust the number of items as desired.


Now you have a single object but they all share UV data and are kept in sync.